Find equation of line which contain the point (2,2) and sum of whose intercept on the coordinate axes is 9. (Please provide me a detailed solution )
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Let a, b the intercepts.
Given that a + b = 9 ---- (1)
We know that equation of a line in the intercept form is x/a + y/b = 1.
Given that the required line is passing through the point (2,2)
2/a + 2/b = 1
2(a + b) = ab
2(9) = ab
ab = 18.
a = 18/b --- (2).
Substitute a = 18/b in (1), we get
18/b + b = 9
18 + b^2 = 9b
b^2 - 9b + 18 = 0
b^2 - 6b - 3b - 18 = 0
b(b-6) - 3(b-6) = 0
b = 3 (or) 6.
Substitute b value in (2), we get
a = 3 (or) 6.
The required equation is x/6 + y/3 = 1 = > x + 2y = 6 (or) x+ 2y - 6 = 0
x/3 + y/6 = 1 = > 2x + y = 6 (or) 2x + y - 6 = 0.
Hope this helps!
Given that a + b = 9 ---- (1)
We know that equation of a line in the intercept form is x/a + y/b = 1.
Given that the required line is passing through the point (2,2)
2/a + 2/b = 1
2(a + b) = ab
2(9) = ab
ab = 18.
a = 18/b --- (2).
Substitute a = 18/b in (1), we get
18/b + b = 9
18 + b^2 = 9b
b^2 - 9b + 18 = 0
b^2 - 6b - 3b - 18 = 0
b(b-6) - 3(b-6) = 0
b = 3 (or) 6.
Substitute b value in (2), we get
a = 3 (or) 6.
The required equation is x/6 + y/3 = 1 = > x + 2y = 6 (or) x+ 2y - 6 = 0
x/3 + y/6 = 1 = > 2x + y = 6 (or) 2x + y - 6 = 0.
Hope this helps!
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